User-friendly biplots in R
Centre for Multi-Dimensional Data Visualisation (MuViSU)
muvisu@sun.ac.za
SASA2024
biplot(state.x77) |> CVA(state.region) |> means(cex = c(1,2,3,4),col = "red",pch = c(9,13,4,16)) |> plot()This function deals with classification regions \ The classify() function appends the biplot object with the following elements: \ - A confusion matrix from the classification into classes - The classification accuracy rate - A logical value indicating whether classification regions are shown in the biplot - A list of chosen aesthetics for the classification regions - The midpoints of the classification regions
class.examp<-biplot(state.x77) |> CVA(state.region) |> classify(col = c("cornflowerblue","darkolivegreen3","darkgoldenrod","aquamarine"))
class.examp$classify# $table
# Reference
# Prediction Northeast South North Central West
# Northeast 8 0 1 0
# South 1 15 0 0
# North Central 1 1 10 0
# West 0 0 0 13
#
# $rate
# Accuracy
# 0.92
#
# $classify.regions
# [1] TRUE
#
# $region.midpoints
# [,1] [,2]
# Northeast 0.12052780 -0.26463306
# South -0.33825365 0.07559722
# North Central 0.07533527 -0.17178605
# West 0.26332961 0.24873651
#
# $aes
# $aes$col
# [1] "#6495ED66" "#A2CD5A66" "#B8860B66" "#7FFFD466"
#
# $aes$opacity
# [1] 0.4
#
# $aes$borders
# [1] FALSE
This function creates \(\alpha\)-bags \ The alpha.bags() function appends the biplot object with the following elements: \ - A list of coordinates for the \(\alpha\)-bags for each group - A vector of colours for the \(\alpha\)-bags - A vector of line types for the \(\alpha\)-bags - A vector of line widths for the \(\alpha\)-bags
ab.examp<-biplot(state.x77) |> CVA(state.region) |> alpha.bags(alpha = c(0.85,0.9,0.95,0.99),lty = c(1,2,3,4))# Computing 0.85 -bag for Northeast
# Computing 0.9 -bag for South
# Computing 0.95 -bag for North Central
# Computing 0.99 -bag for West
# $`Northeast-0.85`
# [,1] [,2]
# [1,] 0.16633269 -0.34121856
# [2,] 0.08880408 -0.38102939
# [3,] 0.04707484 -0.39691735
# [4,] 0.04262374 -0.39694881
# [5,] 0.01983496 -0.39710802
# [6,] -0.08658833 -0.37469874
# [7,] -0.08658829 -0.37469774
# [8,] 0.09848353 -0.15078535
# [9,] 0.16580200 -0.07804116
# [10,] 0.19860357 -0.10560387
# [11,] 0.26022465 -0.17946223
# [12,] 0.26351202 -0.18511612
# [13,] 0.26351247 -0.18511719
# [14,] 0.26668494 -0.20058334
# [15,] 0.26668476 -0.20058463
# [16,] 0.24892584 -0.22957517
#
# $`South-0.9`
# [,1] [,2]
# -0.04734292 0.036516134
# -0.04734302 0.036514770
# -0.09992945 -0.015024416
# -0.14927508 -0.051432512
# -0.22354495 -0.077942971
# -0.36599759 -0.117362800
# -0.48735239 -0.094678439
# -0.49976670 -0.091177816
# -0.50438984 -0.088476626
# sl -0.51619403 -0.075945622
# sl -0.52200140 0.005174029
# -0.52218463 0.011746394
# -0.52497645 0.129443574
# -0.52222437 0.325730381
# -0.52222433 0.325731539
# -0.36858212 0.296091464
# -0.36027380 0.293499192
# -0.34582110 0.288915878
# -0.19220404 0.227718399
# -0.13009266 0.158795901
# -0.07507638 0.091283070
# -0.07507559 0.091281684
#
# $`North Central-0.95`
# [,1] [,2]
# [1,] 0.24022097 -0.121798637
# [2,] 0.24041247 -0.124853201
# [3,] 0.24198566 -0.149997207
# [4,] 0.24198571 -0.149998765
# [5,] 0.23824746 -0.268840097
# [6,] 0.23824740 -0.268841560
# [7,] 0.17747475 -0.327065706
# [8,] 0.01269478 -0.468235431
# [9,] -0.13241334 -0.165868998
# [10,] -0.20722221 0.005971102
# [11,] -0.20722222 0.005972554
# [12,] -0.11418651 0.022533061
# [13,] -0.06574489 0.028766686
# [14,] 0.03116764 0.041193137
# [15,] 0.18315932 0.051420222
# [16,] 0.22798305 -0.040029586
# [17,] 0.23609112 -0.060956142
#
# $`West-0.99`
# [,1] [,2]
# sr 0.40944473 0.09343949
# sr 0.40064366 0.08212953
# 0.38322828 0.06051974
# 0.36382821 0.06015583
# 0.35085860 0.06002291
# 0.33792742 0.06007482
# 0.32212424 0.06450568
# 0.32024851 0.06503188
# 0.28759382 0.07446779
# 0.21595645 0.09575543
# 0.17883496 0.14824762
# sl 0.10634397 0.25255297
# sl 0.08153650 0.28871482
# sl 0.08153649 0.28871637
# sl 0.08404261 0.36108532
# 0.08659044 0.41386061
# 0.08694699 0.42055496
# 0.10654148 0.43414262
# 0.13067615 0.45058965
# 0.35702476 0.60138841
# 0.46904566 0.33475158
# 0.50543483 0.24615210
# sr 0.51318505 0.22695613
# sr 0.51318505 0.22695458
This function creates \(\kappa\)-ellipses \ The alpha.bags() function appends the biplot object with the following elements: \ - A list of coordinates for the \(\kappa\)-bags for each group - A vector of colours for the \(\kappa\)-bags - A vector of line types for the \(\kappa\)-bags - A vector of line widths for the \(\kappa\)-bags - A vector of \(\alpha\) values
kc.examp<-biplot(state.x77) |> CVA(state.region) |> ellipses(alpha = c(0.85,0.9,0.95,0.99),lwd = c(1,2,3,4))# Computing 1.95 -ellipse for Northeast
# Computing 2.15 -ellipse for South
# Computing 2.45 -ellipse for North Central
# Computing 3.03 -ellipse for West
# $`Northeast-1.95`
# [,1] [,2]
# [1,] -0.1104009263 -0.48947500
# [2,] -0.1113637518 -0.48846301
# [3,] -0.1123033884 -0.48742863
# [4,] -0.1132197420 -0.48637198
# [5,] -0.1141127211 -0.48529315
# [6,] -0.1149822363 -0.48419226
# [7,] -0.1158282008 -0.48306941
# [8,] -0.1166505298 -0.48192472
# [9,] -0.1174491412 -0.48075829
# [10,] -0.1182239550 -0.47957026
# [11,] -0.1189748939 -0.47836073
# [12,] -0.1197018828 -0.47712983
# [13,] -0.1204048488 -0.47587768
# [14,] -0.1210837219 -0.47460441
# [15,] -0.1217384339 -0.47331014
# [16,] -0.1223689195 -0.47199500
# [17,] -0.1229751157 -0.47065913
# [18,] -0.1235569618 -0.46930265
# [19,] -0.1241143996 -0.46792571
# [20,] -0.1246473734 -0.46652844
# [21,] -0.1251558298 -0.46511097
# [22,] -0.1256397182 -0.46367346
# [23,] -0.1260989899 -0.46221605
# [24,] -0.1265335992 -0.46073888
# [25,] -0.1269435026 -0.45924210
# [26,] -0.1273286590 -0.45772586
# [27,] -0.1276890300 -0.45619030
# [28,] -0.1280245796 -0.45463560
# [29,] -0.1283352741 -0.45306189
# [30,] -0.1286210824 -0.45146934
# [31,] -0.1288819762 -0.44985811
# [32,] -0.1291179291 -0.44822835
# [33,] -0.1293289177 -0.44658023
# [34,] -0.1295149208 -0.44491392
# [35,] -0.1296759199 -0.44322959
# [36,] -0.1298118988 -0.44152739
# [37,] -0.1299228439 -0.43980750
# [38,] -0.1300087442 -0.43807010
# [39,] -0.1300695910 -0.43631535
# [40,] -0.1301053783 -0.43454344
# [41,] -0.1301161025 -0.43275453
# [42,] -0.1301017625 -0.43094881
# [43,] -0.1300623598 -0.42912646
# [44,] -0.1299978982 -0.42728766
# [45,] -0.1299083843 -0.42543260
# [46,] -0.1297938270 -0.42356145
# [47,] -0.1296542377 -0.42167442
# [48,] -0.1294896305 -0.41977167
# [49,] -0.1293000217 -0.41785342
# [50,] -0.1290854303 -0.41591984
# [51,] -0.1288458778 -0.41397114
# [52,] -0.1285813882 -0.41200750
# [53,] -0.1282919878 -0.41002912
# [54,] -0.1279777057 -0.40803621
# [55,] -0.1276385732 -0.40602895
# [56,] -0.1272746243 -0.40400756
# [57,] -0.1268858954 -0.40197222
# [58,] -0.1264724253 -0.39992316
# [59,] -0.1260342554 -0.39786056
# [60,] -0.1255714294 -0.39578464
# [61,] -0.1250839938 -0.39369561
# [62,] -0.1245719972 -0.39159367
# [63,] -0.1240354908 -0.38947904
# [64,] -0.1234745283 -0.38735192
# [65,] -0.1228891658 -0.38521253
# [66,] -0.1222794617 -0.38306108
# [67,] -0.1216454772 -0.38089778
# [68,] -0.1209872755 -0.37872287
# [69,] -0.1203049225 -0.37653654
# [70,] -0.1195984865 -0.37433902
# [71,] -0.1188680380 -0.37213053
# [72,] -0.1181136501 -0.36991130
# [73,] -0.1173353983 -0.36768153
# [74,] -0.1165333604 -0.36544146
# [75,] -0.1157076165 -0.36319131
# [76,] -0.1148582493 -0.36093130
# [77,] -0.1139853437 -0.35866167
# [78,] -0.1130889870 -0.35638263
# [79,] -0.1121692688 -0.35409441
# [80,] -0.1112262811 -0.35179725
# [81,] -0.1102601181 -0.34949138
# [82,] -0.1092708766 -0.34717701
# [83,] -0.1082586554 -0.34485440
# [84,] -0.1072235557 -0.34252376
# [85,] -0.1061656811 -0.34018533
# [86,] -0.1050851373 -0.33783935
# [87,] -0.1039820325 -0.33548605
# [88,] -0.1028564768 -0.33312566
# [89,] -0.1017085829 -0.33075842
# [90,] -0.1005384655 -0.32838457
# [91,] -0.0993462417 -0.32600434
# [92,] -0.0981320307 -0.32361798
# [93,] -0.0968959538 -0.32122572
# [94,] -0.0956381348 -0.31882780
# [95,] -0.0943586994 -0.31642446
# [96,] -0.0930577755 -0.31401594
# [97,] -0.0917354932 -0.31160249
# [98,] -0.0903919848 -0.30918433
# [99,] -0.0890273845 -0.30676172
# [100,] -0.0876418289 -0.30433490
# [101,] -0.0862354566 -0.30190411
# [102,] -0.0848084080 -0.29946959
# [103,] -0.0833608261 -0.29703159
# [104,] -0.0818928554 -0.29459035
# [105,] -0.0804046428 -0.29214611
# [106,] -0.0788963372 -0.28969912
# [107,] -0.0773680893 -0.28724962
# [108,] -0.0758200520 -0.28479786
# [109,] -0.0742523801 -0.28234409
# [110,] -0.0726652303 -0.27988855
# [111,] -0.0710587614 -0.27743148
# [112,] -0.0694331339 -0.27497312
# [113,] -0.0677885106 -0.27251374
# [114,] -0.0661250557 -0.27005357
# [115,] -0.0644429358 -0.26759285
# [116,] -0.0627423189 -0.26513184
# [117,] -0.0610233752 -0.26267078
# [118,] -0.0592862764 -0.26020992
# [119,] -0.0575311965 -0.25774950
# [120,] -0.0557583108 -0.25528976
# [121,] -0.0539677966 -0.25283096
# [122,] -0.0521598330 -0.25037334
# [123,] -0.0503346008 -0.24791715
# [124,] -0.0484922825 -0.24546263
# [125,] -0.0466330623 -0.24301003
# [126,] -0.0447571262 -0.24055958
# [127,] -0.0428646617 -0.23811155
# [128,] -0.0409558581 -0.23566617
# [129,] -0.0390309063 -0.23322368
# [130,] -0.0370899987 -0.23078433
# [131,] -0.0351333295 -0.22834837
# [132,] -0.0331610943 -0.22591604
# [133,] -0.0311734904 -0.22348758
# [134,] -0.0291707165 -0.22106324
# [135,] -0.0271529728 -0.21864325
# [136,] -0.0251204611 -0.21622786
# [137,] -0.0230733848 -0.21381731
# [138,] -0.0210119485 -0.21141184
# [139,] -0.0189363583 -0.20901169
# [140,] -0.0168468218 -0.20661711
# [141,] -0.0147435480 -0.20422833
# [142,] -0.0126267471 -0.20184559
# [143,] -0.0104966309 -0.19946912
# [144,] -0.0083534124 -0.19709918
# [145,] -0.0061973058 -0.19473598
# [146,] -0.0040285269 -0.19237978
# [147,] -0.0018472924 -0.19003080
# [148,] 0.0003461795 -0.18768928
# [149,] 0.0025516695 -0.18535546
# [150,] 0.0047689569 -0.18302956
# [151,] 0.0069978202 -0.18071183
# [152,] 0.0092380363 -0.17840248
# [153,] 0.0114893814 -0.17610176
# [154,] 0.0137516302 -0.17380990
# [155,] 0.0160245565 -0.17152711
# [156,] 0.0183079330 -0.16925364
# [157,] 0.0206015315 -0.16698970
# [158,] 0.0229051225 -0.16473553
# [159,] 0.0252184757 -0.16249134
# [160,] 0.0275413597 -0.16025737
# [161,] 0.0298735423 -0.15803384
# [162,] 0.0322147903 -0.15582097
# [163,] 0.0345648694 -0.15361898
# [164,] 0.0369235448 -0.15142809
# [165,] 0.0392905806 -0.14924852
# [166,] 0.0416657400 -0.14708049
# [167,] 0.0440487856 -0.14492421
# [168,] 0.0464394789 -0.14277991
# [169,] 0.0488375811 -0.14064779
# [170,] 0.0512428522 -0.13852807
# [171,] 0.0536550518 -0.13642096
# [172,] 0.0560739386 -0.13432667
# [173,] 0.0584992707 -0.13224541
# [174,] 0.0609308056 -0.13017739
# [175,] 0.0633683001 -0.12812281
# [176,] 0.0658115106 -0.12608189
# [177,] 0.0682601926 -0.12405482
# [178,] 0.0707141014 -0.12204181
# [179,] 0.0731729915 -0.12004306
# [180,] 0.0756366170 -0.11805876
# [181,] 0.0781047316 -0.11608913
# [182,] 0.0805770885 -0.11413435
# [183,] 0.0830534404 -0.11219461
# [184,] 0.0855335397 -0.11027013
# [185,] 0.0880171384 -0.10836107
# [186,] 0.0905039882 -0.10646765
# [187,] 0.0929938403 -0.10459004
# [188,] 0.0954864458 -0.10272844
# [189,] 0.0979815554 -0.10088302
# [190,] 0.1004789196 -0.09905398
# [191,] 0.1029782887 -0.09724150
# [192,] 0.1054794127 -0.09544576
# [193,] 0.1079820415 -0.09366693
# [194,] 0.1104859249 -0.09190521
# [195,] 0.1129908125 -0.09016075
# [196,] 0.1154964538 -0.08843374
# [197,] 0.1180025982 -0.08672435
# [198,] 0.1205089951 -0.08503276
# [199,] 0.1230153939 -0.08335912
# [200,] 0.1255215440 -0.08170361
# [201,] 0.1280271946 -0.08006639
# [202,] 0.1305320954 -0.07844763
# [203,] 0.1330359957 -0.07684749
# [204,] 0.1355386452 -0.07526613
# [205,] 0.1380397937 -0.07370370
# [206,] 0.1405391909 -0.07216036
# [207,] 0.1430365870 -0.07063628
# [208,] 0.1455317323 -0.06913159
# [209,] 0.1480243772 -0.06764645
# [210,] 0.1505142725 -0.06618101
# [211,] 0.1530011691 -0.06473541
# [212,] 0.1554848184 -0.06330981
# [213,] 0.1579649721 -0.06190434
# [214,] 0.1604413821 -0.06051914
# [215,] 0.1629138007 -0.05915435
# [216,] 0.1653819808 -0.05781011
# [217,] 0.1678456755 -0.05648655
# [218,] 0.1703046384 -0.05518380
# [219,] 0.1727586237 -0.05390200
# [220,] 0.1752073860 -0.05264128
# [221,] 0.1776506804 -0.05140175
# [222,] 0.1800882625 -0.05018354
# [223,] 0.1825198886 -0.04898678
# [224,] 0.1849453155 -0.04781159
# [225,] 0.1873643008 -0.04665807
# [226,] 0.1897766025 -0.04552636
# [227,] 0.1921819793 -0.04441655
# [228,] 0.1945801908 -0.04332877
# [229,] 0.1969709971 -0.04226311
# [230,] 0.1993541592 -0.04121969
# [231,] 0.2017294386 -0.04019862
# [232,] 0.2040965980 -0.03919998
# [233,] 0.2064554006 -0.03822389
# [234,] 0.2088056105 -0.03727045
# [235,] 0.2111469926 -0.03633973
# [236,] 0.2134793130 -0.03543185
# [237,] 0.2158023382 -0.03454688
# [238,] 0.2181158361 -0.03368493
# [239,] 0.2204195753 -0.03284607
# [240,] 0.2227133253 -0.03203039
# [241,] 0.2249968569 -0.03123796
# [242,] 0.2272699417 -0.03046888
# [243,] 0.2295323524 -0.02972321
# [244,] 0.2317838627 -0.02900104
# [245,] 0.2340242474 -0.02830242
# [246,] 0.2362532827 -0.02762744
# [247,] 0.2384707454 -0.02697616
# [248,] 0.2406764140 -0.02634865
# [249,] 0.2428700678 -0.02574496
# [250,] 0.2450514875 -0.02516517
# [251,] 0.2472204549 -0.02460931
# [252,] 0.2493767532 -0.02407747
# [253,] 0.2515201667 -0.02356967
# [254,] 0.2536504810 -0.02308598
# [255,] 0.2557674832 -0.02262645
# [256,] 0.2578709615 -0.02219112
# [257,] 0.2599607057 -0.02178003
# [258,] 0.2620365066 -0.02139323
# [259,] 0.2640981568 -0.02103075
# [260,] 0.2661454501 -0.02069263
# [261,] 0.2681781818 -0.02037890
# [262,] 0.2701961485 -0.02008960
# [263,] 0.2721991485 -0.01982476
# [264,] 0.2741869815 -0.01958439
# [265,] 0.2761594487 -0.01936853
# [266,] 0.2781163529 -0.01917720
# [267,] 0.2800574984 -0.01901041
# [268,] 0.2819826910 -0.01886818
# [269,] 0.2838917383 -0.01875053
# [270,] 0.2857844493 -0.01865747
# [271,] 0.2876606348 -0.01858900
# [272,] 0.2895201071 -0.01854514
# [273,] 0.2913626803 -0.01852589
# [274,] 0.2931881702 -0.01853124
# [275,] 0.2949963943 -0.01856121
# [276,] 0.2967871715 -0.01861579
# [277,] 0.2985603230 -0.01869496
# [278,] 0.3003156714 -0.01879873
# [279,] 0.3020530412 -0.01892709
# [280,] 0.3037722586 -0.01908001
# [281,] 0.3054731517 -0.01925749
# [282,] 0.3071555504 -0.01945950
# [283,] 0.3088192865 -0.01968604
# [284,] 0.3104641936 -0.01993706
# [285,] 0.3120901072 -0.02021256
# [286,] 0.3136968648 -0.02051250
# [287,] 0.3152843056 -0.02083685
# [288,] 0.3168522709 -0.02118558
# [289,] 0.3184006039 -0.02155865
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# [589,] -0.0536539769 -0.51071133
# [590,] -0.0554475449 -0.51066068
# [591,] -0.0572235155 -0.51058542
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# [597,] -0.0674999740 -0.50961781
# [598,] -0.0691478910 -0.50937068
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# [601,] -0.0739771877 -0.50848257
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# [603,] -0.0770997356 -0.50776852
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# [608,] -0.0845576143 -0.50555864
# [609,] -0.0859882514 -0.50504420
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# [627,] -0.1080799139 -0.49173467
# [628,] -0.1090961294 -0.49077496
# [629,] -0.1100893828 -0.48979263
#
# $`South-2.15`
# [,1] [,2]
# [1,] -7.106971e-01 1.090893e-01
# [2,] -7.104026e-01 1.121559e-01
# [3,] -7.100708e-01 1.152188e-01
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# [5,] -7.092958e-01 1.213324e-01
# [6,] -7.088526e-01 1.243825e-01
# [7,] -7.083724e-01 1.274277e-01
# [8,] -7.078552e-01 1.304678e-01
# [9,] -7.073009e-01 1.335023e-01
# [10,] -7.067098e-01 1.365311e-01
# [11,] -7.060819e-01 1.395537e-01
# [12,] -7.054171e-01 1.425700e-01
# [13,] -7.047157e-01 1.455796e-01
# [14,] -7.039776e-01 1.485821e-01
# [15,] -7.032029e-01 1.515774e-01
# [16,] -7.023917e-01 1.545651e-01
# [17,] -7.015441e-01 1.575449e-01
# [18,] -7.006602e-01 1.605165e-01
# [19,] -6.997401e-01 1.634796e-01
# [20,] -6.987838e-01 1.664339e-01
# [21,] -6.977914e-01 1.693791e-01
# [22,] -6.967631e-01 1.723149e-01
# [23,] -6.956990e-01 1.752411e-01
# [24,] -6.945991e-01 1.781573e-01
# [25,] -6.934635e-01 1.810633e-01
# [26,] -6.922925e-01 1.839587e-01
# [27,] -6.910860e-01 1.868432e-01
# [28,] -6.898443e-01 1.897167e-01
# [29,] -6.885674e-01 1.925787e-01
# [30,] -6.872554e-01 1.954290e-01
# [31,] -6.859086e-01 1.982674e-01
# [32,] -6.845270e-01 2.010935e-01
# [33,] -6.831108e-01 2.039070e-01
# [34,] -6.816601e-01 2.067077e-01
# [35,] -6.801750e-01 2.094953e-01
# [36,] -6.786558e-01 2.122695e-01
# [37,] -6.771025e-01 2.150300e-01
# [38,] -6.755153e-01 2.177766e-01
# [39,] -6.738944e-01 2.205090e-01
# [40,] -6.722400e-01 2.232269e-01
# [41,] -6.705521e-01 2.259300e-01
# [42,] -6.688310e-01 2.286181e-01
# [43,] -6.670769e-01 2.312909e-01
# [44,] -6.652898e-01 2.339481e-01
# [45,] -6.634701e-01 2.365895e-01
# [46,] -6.616179e-01 2.392148e-01
# [47,] -6.597333e-01 2.418237e-01
# [48,] -6.578165e-01 2.444160e-01
# [49,] -6.558679e-01 2.469914e-01
# [50,] -6.538874e-01 2.495497e-01
# [51,] -6.518754e-01 2.520906e-01
# [52,] -6.498320e-01 2.546138e-01
# [53,] -6.477575e-01 2.571191e-01
# [54,] -6.456520e-01 2.596063e-01
# [55,] -6.435158e-01 2.620751e-01
# [56,] -6.413490e-01 2.645252e-01
# [57,] -6.391520e-01 2.669565e-01
# [58,] -6.369248e-01 2.693686e-01
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# [604,] -7.057348e-01 3.116453e-02
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# [628,] -7.110285e-01 1.050409e-01
# [629,] -7.107831e-01 1.081118e-01
#
# $`North Central-2.45`
# [,1] [,2]
# [1,] -0.115309509 1.741007e-01
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# [21,] -0.052151781 1.999225e-01
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# [110,] 0.252067234 1.341896e-01
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# [119,] 0.278963549 1.122332e-01
# [120,] 0.281854143 1.096483e-01
# [121,] 0.284724084 1.070352e-01
# [122,] 0.287573087 1.043942e-01
# [123,] 0.290400867 1.017256e-01
# [124,] 0.293207140 9.902966e-02
# [125,] 0.295991626 9.630664e-02
# [126,] 0.298754046 9.355681e-02
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# [128,] 0.304211588 8.797782e-02
# [129,] 0.306906164 8.514922e-02
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# [131,] 0.312225578 7.941523e-02
# [132,] 0.314849884 7.651041e-02
# [133,] 0.317450238 7.358076e-02
# [134,] 0.320026382 7.062658e-02
# [135,] 0.322578056 6.764815e-02
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# [513,] -0.274536549 -1.858568e-01
# [514,] -0.275084903 -1.820278e-01
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# [516,] -0.276076432 -1.743673e-01
# [517,] -0.276519510 -1.705364e-01
# [518,] -0.276927402 -1.667057e-01
# [519,] -0.277300068 -1.628754e-01
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# [523,] -0.278437782 -1.475673e-01
# [524,] -0.278633830 -1.437453e-01
# [525,] -0.278794481 -1.399262e-01
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# [529,] -0.279082852 -1.246853e-01
# [530,] -0.279066351 -1.208859e-01
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# [534,] -0.278646014 -1.057430e-01
# [535,] -0.278452401 -1.019729e-01
# [536,] -0.278223408 -9.820968e-02
# [537,] -0.277959061 -9.445386e-02
# [538,] -0.277659384 -9.070577e-02
# [539,] -0.277324408 -8.696579e-02
# [540,] -0.276954166 -8.323430e-02
# [541,] -0.276548695 -7.951165e-02
# [542,] -0.276108037 -7.579824e-02
# [543,] -0.275632234 -7.209442e-02
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# [545,] -0.274575391 -6.471707e-02
# [546,] -0.273994456 -6.104427e-02
# [547,] -0.273378588 -5.738254e-02
# [548,] -0.272727849 -5.373225e-02
# [549,] -0.272042304 -5.009377e-02
# [550,] -0.271322021 -4.646746e-02
# [551,] -0.270567073 -4.285368e-02
# [552,] -0.269777536 -3.925279e-02
# [553,] -0.268953487 -3.566515e-02
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# [563,] -0.258834720 -5.959595e-04
# [564,] -0.257637242 2.822529e-03
# [565,] -0.256406467 6.223556e-03
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# [567,] -0.253845521 1.297187e-02
# [568,] -0.252515607 1.631848e-02
# [569,] -0.251152907 1.964628e-02
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# [572,] -0.246869480 2.951351e-02
# [573,] -0.245377037 3.276276e-02
# [574,] -0.243852523 3.599156e-02
# [575,] -0.242296090 3.919958e-02
# [576,] -0.240707895 4.238650e-02
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# [578,] -0.237436853 4.869577e-02
# [579,] -0.235754335 5.181749e-02
# [580,] -0.234040708 5.491686e-02
# [581,] -0.232296143 5.799355e-02
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# [585,] -0.225012046 7.006750e-02
# [586,] -0.223115473 7.302627e-02
# [587,] -0.221189055 7.596056e-02
# [588,] -0.219232985 7.887008e-02
# [589,] -0.217247458 8.175453e-02
# [590,] -0.215232673 8.461363e-02
# [591,] -0.213188832 8.744709e-02
# [592,] -0.211116138 9.025463e-02
# [593,] -0.209014799 9.303596e-02
# [594,] -0.206885026 9.579081e-02
# [595,] -0.204727031 9.851890e-02
# [596,] -0.202541030 1.012200e-01
# [597,] -0.200327242 1.038937e-01
# [598,] -0.198085887 1.065399e-01
# [599,] -0.195817191 1.091583e-01
# [600,] -0.193521379 1.117485e-01
# [601,] -0.191198683 1.143105e-01
# [602,] -0.188849333 1.168438e-01
# [603,] -0.186473564 1.193482e-01
# [604,] -0.184071615 1.218235e-01
# [605,] -0.181643726 1.242695e-01
# [606,] -0.179190139 1.266859e-01
# [607,] -0.176711100 1.290724e-01
# [608,] -0.174206856 1.314288e-01
# [609,] -0.171677658 1.337549e-01
# [610,] -0.169123759 1.360505e-01
# [611,] -0.166545414 1.383152e-01
# [612,] -0.163942882 1.405490e-01
# [613,] -0.161316422 1.427515e-01
# [614,] -0.158666297 1.449226e-01
# [615,] -0.155992772 1.470620e-01
# [616,] -0.153296114 1.491695e-01
# [617,] -0.150576594 1.512450e-01
# [618,] -0.147834482 1.532881e-01
# [619,] -0.145070054 1.552987e-01
# [620,] -0.142283585 1.572766e-01
# [621,] -0.139475355 1.592216e-01
# [622,] -0.136645643 1.611335e-01
# [623,] -0.133794734 1.630121e-01
# [624,] -0.130922912 1.648572e-01
# [625,] -0.128030464 1.666687e-01
# [626,] -0.125117680 1.684463e-01
# [627,] -0.122184851 1.701899e-01
# [628,] -0.119232270 1.718993e-01
# [629,] -0.116260232 1.735744e-01
#
# $`West-3.03`
# [,1] [,2]
# [1,] 0.0992973469 0.7070334492
# [2,] 0.1026709401 0.7082150654
# [3,] 0.1060605990 0.7093507341
# [4,] 0.1094659847 0.7104403418
# [5,] 0.1128867567 0.7114837795
# [6,] 0.1163225728 0.7124809428
# [7,] 0.1197730895 0.7134317321
# [8,] 0.1232379617 0.7143360523
# [9,] 0.1267168430 0.7151938129
# [10,] 0.1302093855 0.7160049281
# [11,] 0.1337152398 0.7167693169
# [12,] 0.1372340555 0.7174869028
# [13,] 0.1407654806 0.7181576141
# [14,] 0.1443091621 0.7187813836
# [15,] 0.1478647454 0.7193581490
# [16,] 0.1514318752 0.7198878527
# [17,] 0.1550101947 0.7203704416
# [18,] 0.1585993460 0.7208058675
# [19,] 0.1621989702 0.7211940869
# [20,] 0.1658087075 0.7215350609
# [21,] 0.1694281967 0.7218287555
# [22,] 0.1730570760 0.7220751412
# [23,] 0.1766949825 0.7222741935
# [24,] 0.1803415523 0.7224258924
# [25,] 0.1839964209 0.7225302227
# [26,] 0.1876592228 0.7225871740
# [27,] 0.1913295916 0.7225967407
# [28,] 0.1950071604 0.7225589218
# [29,] 0.1986915614 0.7224737210
# [30,] 0.2023824261 0.7223411469
# [31,] 0.2060793855 0.7221612127
# [32,] 0.2097820698 0.7219339364
# [33,] 0.2134901089 0.7216593408
# [34,] 0.2172031319 0.7213374533
# [35,] 0.2209207674 0.7209683061
# [36,] 0.2246426439 0.7205519362
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# [38,] 0.2320976302 0.7195776991
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# [41,] 0.2433025996 0.7177633667
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# [47,] 0.2657565073 0.7128704371
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# [49,] 0.2732431947 0.7108672213
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# [51,] 0.2807259169 0.7086791594
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# [53,] 0.2882016808 0.7063071266
# [54,] 0.2919360188 0.7050524147
# [55,] 0.2956674962 0.7037520716
# [56,] 0.2993957398 0.7024062273
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# [59,] 0.3105573417 0.6980970559
# [60,] 0.3142689258 0.6965705980
# [61,] 0.3179754161 0.6949993571
# [62,] 0.3216764418 0.6933834903
# [63,] 0.3253716329 0.6917231592
# [64,] 0.3290606199 0.6900185297
# [65,] 0.3327430338 0.6882697725
# [66,] 0.3364185064 0.6864770622
# [67,] 0.3400866702 0.6846405783
# [68,] 0.3437471583 0.6827605043
# [69,] 0.3473996048 0.6808370283
# [70,] 0.3510436443 0.6788703426
# [71,] 0.3546789125 0.6768606439
# [72,] 0.3583050458 0.6748081331
# [73,] 0.3619216817 0.6727130155
# [74,] 0.3655284584 0.6705755007
# [75,] 0.3691250154 0.6683958022
# [76,] 0.3727109929 0.6661741382
# [77,] 0.3762860323 0.6639107308
# [78,] 0.3798497762 0.6616058063
# [79,] 0.3834018682 0.6592595952
# [80,] 0.3869419531 0.6568723321
# [81,] 0.3904696768 0.6544442558
# [82,] 0.3939846866 0.6519756091
# [83,] 0.3974866310 0.6494666388
# [84,] 0.4009751599 0.6469175958
# [85,] 0.4044499243 0.6443287350
# [86,] 0.4079105768 0.6417003154
# [87,] 0.4113567713 0.6390325997
# [88,] 0.4147881632 0.6363258547
# [89,] 0.4182044094 0.6335803510
# [90,] 0.4216051682 0.6307963634
# [91,] 0.4249900996 0.6279741700
# [92,] 0.4283588651 0.6251140532
# [93,] 0.4317111278 0.6222162990
# [94,] 0.4350465525 0.6192811971
# [95,] 0.4383648056 0.6163090410
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# [98,] 0.4482132263 0.6071732384
# [99,] 0.4514594927 0.6040558744
# [100,] 0.4546869462 0.6009029788
# [101,] 0.4578952642 0.5977148668
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# [103,] 0.4642532121 0.5912342726
# [104,] 0.4674022062 0.5879424383
# [105,] 0.4705307932 0.5846166838
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# [107,] 0.4767254966 0.5778647474
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# [111,] 0.4888563931 0.5639686872
# [112,] 0.4918334887 0.5604149882
# [113,] 0.4947877341 0.5568301217
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# [115,] 0.5006264950 0.5495683228
# [116,] 0.5035104265 0.5458921166
# [117,] 0.5063703402 0.5421861952
# [118,] 0.5092059500 0.5384509290
# [119,] 0.5120169724 0.5346866916
# [120,] 0.5148031263 0.5308938595
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# [122,] 0.5202997165 0.5232239307
# [123,] 0.5230096031 0.5193476012
# [124,] 0.5256935220 0.5154442107
# [125,] 0.5283512047 0.5115141497
# [126,] 0.5309823855 0.5075578112
# [127,] 0.5335868013 0.5035755907
# [128,] 0.5361641915 0.4995678865
# [129,] 0.5387142985 0.4955350994
# [130,] 0.5412368672 0.4914776327
# [131,] 0.5437316455 0.4873958920
# [132,] 0.5461983838 0.4832902856
# [133,] 0.5486368355 0.4791612241
# [134,] 0.5510467566 0.4750091202
# [135,] 0.5534279063 0.4708343893
# [136,] 0.5557800464 0.4666374487
# [137,] 0.5581029418 0.4624187183
# [138,] 0.5603963600 0.4581786198
# [139,] 0.5626600718 0.4539175773
# [140,] 0.5648938508 0.4496360168
# [141,] 0.5670974736 0.4453343666
# [142,] 0.5692707199 0.4410130567
# [143,] 0.5714133723 0.4366725193
# [144,] 0.5735252166 0.4323131885
# [145,] 0.5756060416 0.4279355002
# [146,] 0.5776556393 0.4235398921
# [147,] 0.5796738046 0.4191268039
# [148,] 0.5816603357 0.4146966767
# [149,] 0.5836150340 0.4102499537
# [150,] 0.5855377041 0.4057870794
# [151,] 0.5874281536 0.4013085003
# [152,] 0.5892861935 0.3968146640
# [153,] 0.5911116380 0.3923060201
# [154,] 0.5929043047 0.3877830193
# [155,] 0.5946640141 0.3832461140
# [156,] 0.5963905903 0.3786957579
# [157,] 0.5980838607 0.3741324059
# [158,] 0.5997436560 0.3695565144
# [159,] 0.6013698102 0.3649685411
# [160,] 0.6029621606 0.3603689446
# [161,] 0.6045205481 0.3557581850
# [162,] 0.6060448167 0.3511367233
# [163,] 0.6075348141 0.3465050217
# [164,] 0.6089903913 0.3418635433
# [165,] 0.6104114026 0.3372127523
# [166,] 0.6117977061 0.3325531137
# [167,] 0.6131491631 0.3278850935
# [168,] 0.6144656384 0.3232091586
# [169,] 0.6157470004 0.3185257764
# [170,] 0.6169931210 0.3138354154
# [171,] 0.6182038754 0.3091385445
# [172,] 0.6193791428 0.3044356335
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# [175,] 0.6226908647 0.2902953651
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# [183,] 0.6299338806 0.2524398018
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# [187,] 0.6326783200 0.2334879787
# [188,] 0.6332722557 0.2287526507
# [189,] 0.6338291975 0.2240193211
# [190,] 0.6343490897 0.2192884632
# [191,] 0.6348318802 0.2145605501
# [192,] 0.6352775208 0.2098360545
# [193,] 0.6356859669 0.2051154489
# [194,] 0.6360571777 0.2003992054
# [195,] 0.6363911161 0.1956877956
# [196,] 0.6366877486 0.1909816906
# [197,] 0.6369470456 0.1862813611
# [198,] 0.6371689812 0.1815872770
# [199,] 0.6373535331 0.1768999078
# [200,] 0.6375006830 0.1722197222
# [201,] 0.6376104160 0.1675471882
# [202,] 0.6376827213 0.1628827730
# [203,] 0.6377175917 0.1582269432
# [204,] 0.6377150235 0.1535801642
# [205,] 0.6376750171 0.1489429008
# [206,] 0.6375975764 0.1443156167
# [207,] 0.6374827093 0.1396987746
# [208,] 0.6373304272 0.1350928361
# [209,] 0.6371407453 0.1304982620
# [210,] 0.6369136826 0.1259155115
# [211,] 0.6366492618 0.1213450431
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# [213,] 0.6360084554 0.1122427791
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# [215,] 0.6352185825 0.1031951107
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# [240,] 0.6129658201 -0.0038491827
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